Ucwaningo oluphelele lwemisebenzi futhi umehluko calculus

Ukuba ngolwazi olunzulu izici ukuba sibeke ahlomile ehamba ngezinqola ithuluzi eyanele ukuze afeze ucwaningo ephelele ngokuqondile amaphethini izibalo predetermined ngesimo ifomula (umsebenzi). Yiqiniso, omunye angase ahambe indlela elula kunazo kodwa kukhathaza. Ngokwesibonelo, unikezwa ububanzi agumenti khetha isikhawu, ukubala value umsebenzi kuso futhi ukwakha igrafu. Ngo nokuba khona enamandla yesimanje tangcondvomshini, lokhu inkinga isixazululekile indaba imizuzwana. Kodwa ukususa arsenal egcwele yayo Ukutadisha umsebenzi wezibalo ekujaheni, ngoba yilezi zindlela zingasetshenziswa ukuhlola ngokunemba ukusebenza kwezinhlelo zekhompyutha ekuxazululeni izinkinga ezinjalo. Ngo ugobe mechanical, asikwazi ukuqinisekisa ukunemba kwesikhathi esishiwo ngenhla uhla agumenti Ukukhetha.

Futhi kuphela ngemuva kophenyo ephelele umsebenzi, ungaqiniseka, ukuthi uyakucabangela zonke ezicashile "ukuziphatha" ayikanye phezu isikhawu izibonelo zalokho, futhi lonke uhla lwama-agumenti.

Ukuze ukuxazulula ezihlukahlukene imisebenzi emikhakheni physics, mathematics kanye nobuchwepheshe kukhona isidingo utadisha ukwencika obusebenzayo phakathi eziguquguqukayo ezazihilelekile kulesi simo. Kugcine, unikezwa analytically elilodwa noma iqoqo amafomula eziningana, ivumela cwaningo izindlela analytics zezibalo.

Ukuze wenze uphenyo olunzulu imisebenzi - ukuthola futhi ukukhomba izindawo lapho kwandisa (incipha), lapho ifinyelela esiphezulu (okungenani), kanye nezinye izici uhlelo yayo.

Kukhona izikimu ezithile, okuyinto ezikhiqizwa isifundo ephelele umsebenzi. Izibonelo izinhlu ucwaningo zezibalo eyenziwa ziyancipha ekutholeni izikhathi cishe ezifanayo. ukuhlaziywa lesilinganisiwe we plan kuhilela izifundo ezilandelayo:

- thola esizindeni umsebenzi, sesenze uphenyo ukuziphatha ngaphakathi kwemingcele yayo;

- sife okwatholakala ikhefu amaphuzu ngezigaba esebenzisa imikhawulo sohlangothi olulodwa;

- ukuze afeze asymptotes ezithile;

- sithola iphuzu extremum futhi monotonicity ngezikhawu;

- ukukhiqiza inflection ezithile, ngezikhawu concavity futhi convexity;

- afeze isheduli ukwakhiwa ngesisekelo imiphumela cwaningo.

Uma sicabanga kuphela amaphoyinti aphezulu we plan kuyafaneleka ukuthi calculus umehluko ubelokhu ithuluzi yimpumelelo kakhulu kufundza imisebenti. Kukhona izixhumanisi ulula ezikhona phakathi ukuziphatha umsebenzi kanye nezici zayo esuselwe. Ukuze uxazulule le nkinga kwanele ukubala esuselwe lokuqala nelesibili.

Cabanga inqubo nezindlela zokuthola ukwehla ngezikhawu, ukwandisa umsebenzi Basaba wathola igama monotony ngezikhawu.

Kwanele ukunquma isibonakaliso esuselwe lokuqala ngesikhathi kwenkathi ethile. Uma lona wesifazane njalo phezu kwe-isikhawu mkhulu kunezinhliziyo zero ke thina singahlulela ngokuphepha monotonic ukwanda umsebenzi kuleli banga, futhi okuphambene nalokho. Amanani Negative we esuselwe lokuqala libhekene njengoba umsebenzi monotonically ngincipha.

Ngosizo ekubalweni nemikhiqizo esiqokiwe indawo ihluzo, ngokuthi mabhamuza nemisebenzi ngilugweda. It is wafakazela ukuthi uma ngokuhamba izibalo etholwe esuselwe umsebenzi okuqhubekayo nemibi, kubonisa ukuthi convexity, ukuqhubeka esuselwe yesibili nokubaluleka kwalo omuhle ibonisa ukuthi concavity igrafu.

Ukuthola isikhathi, uma kukhona ushintsho isibonakaliso esuselwe wesibili, noma ezindaweni lapho ingekho, libonisa ukuzimisela iphuzu Ukuphakama kwephimbo. Lokho kuba umngcele ngezikhawu convexity futhi concavity.

cwaningo Okugcwele umsebenzi akugcini amaphuzu angenhla, kodwa ukusetshenziswa calculus umehluko lula kakhulu kule nqubo. Kulokhu, imiphumela ukuhlaziywa ngezinga elithile esiphezulu ukuzethemba, evumela ukwakha igrafu, okuhambisana ngokuphelele ne izakhiwo imisebenzi yokuhlola.